This is going to be a somewhat experimental post. In class, I mentioned that when solving the type of homework problems encountered in a graduate real analysis course, there are really only about a dozen or so basic tricks and techniques that are used over and over again. But I had not thought to actually try to make these tricks explicit, so I am going to try to compile here a list of some of these techniques here. But this list is going to be far from exhaustive; perhaps if other recent students of real analysis would like to share their own methods, then I encourage you to do so in the comments (even – or especially – if the techniques are somewhat vague and general in nature).

(See also the Tricki for some general mathematical problem solving tips. Once this page matures somewhat, I might migrate it to the Tricki.)

Note: the tricks occur here in no particular order, reflecting the stream-of-consciousness way in which they were arrived at. Indeed, this list will be extended on occasion whenever I find another trick that can be added to this list.

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